“JACOBI DOCET” An issue to honor Jacobi’s bicentennial In May 2005 the Journal of Nonlinear Mathematical Physics will dedicate issue no 2 of volume 12 to Carl Gustav Jacob Jacobi’s bicentennial. The issue will be edited by MC Nucci and PGL Leach.

2004 and 2005 are bicentennials for two famous mathematicians Carl Gustav Jacob Jacobi (born December 10, 1804) and William Rowan Hamilton (born August 4, 1805). A celebration of their individual contributions to mathematics is particularly apt because their names continue to be cited very frequently in the mathematical literature (from 2003 to date, 556 and 316 hits in MathSciNet, respectively). Importantly the extraordinary work of these two great mathematicians, especially Jacobi, has been extremely valuable to and enabled past and recent advances in research in a variety of areas. While a celebration of Hamilton’s bicentennial has been already organized thanks to The Hamilton Mathematics Institute at Trinity College in Dublin, Ireland (see www.hamilton.tcd.ie), nothing has been done to honor Jacobi’s bicentennial except for a special session which will be organized by MC Nucci and P Winternitz at the 111th Annual meeting of the American Mathe- matical Society in January 5-8, 2005 (see www.ams.org/amsmtgs/2091−intro.html).

Jacobi worked in many mathematical areas, which are still actively researched, from special func- tions to number theory, from calculus of variations to astronomy, from differential equations to analytical mechanics, until his premature death on February 18, 1851. Also he was an excellent teacher. In his biography of Jacobi (published in 1904 on the occasion of Jacobi’s first centennial) Koenisberger wrote that Jacobi was always able to captivate the interest of his audience not only because he tied up his audience’s attention by the fascination of his ideas, he conveyed his great amount of knowledge and he revealed new view points, but also because of his happy habit of con- necting the historical development of problems to their manifold solutions, problems which were taken from the most apparently heterogeneous disciplines of mathematical science and critically enlightened. In the words of Dirichlet Jacobi’s lectures are preeminent because of their high level of clarity, not at all the same type of clearness that often goes along with penury of ideas.

The issue will focus on differential equations and their applications to physics and other sciences in the wake of Jacobi’s accomplishments. In the introduction to his lectures on dynamics Jacobi stated that any progress in the theory of differential equations must also bring about a progress in mechanics. In particular the issue will contain state of the art articles on the following two topics: separation of variables for the Hamilton-Jacobi and Schr¨odinger equation in classical and quantum mechanics, respectively, with special attention to Lie’s symmetries and the connection to special functions, the last topic initiated by Jacobi in his search for geodesics on an ellipsoid; Jacobi’s last multiplier and its applications to dynamical systems and classical and quantum mechanics.

There will be some reviews as well as original research papers. Contributions are primarily by invitation, but submissions are also welcome. All contributions will be reviewed by anonymous ref- erees. Contributions should be emailed by November 8, 2004 electronically (namely, as a LaTeX file1)[email protected]. For additional information please contact MC Nucci at [email protected].

1Prospective contributors should use the journal template which can be found at the journal website: www.sm.luth.se/math/JNMP